14,150 research outputs found
On the 'Reality' of Observable Properties
This note contains some initial work on attempting to bring recent
developments in the foundations of quantum mechanics concerning the nature of
the wavefunction within the scope of more logical and structural methods. A
first step involves generalising and reformulating a criterion for the reality
of the wavefunction proposed by Harrigan & Spekkens, which was central to the
PBR theorem. The resulting criterion has several advantages, including the
avoidance of certain technical difficulties relating to sets of measure zero.
By considering the 'reality' not of the wavefunction but of the observable
properties of any ontological physical theory a novel characterisation of
non-locality and contextuality is found.
Secondly, a careful analysis of preparation independence, one of the key
assumptions of the PBR theorem, leads to an analogy with Bell locality, and
thence to a proposal to weaken it to an assumption of
`no-preparation-signalling' in analogy with no-signalling. This amounts to
introducing non-local correlations in the joint ontic state, which is, at
least, consistent with the Bell and Kochen-Specker theorems. The question of
whether the PBR result can be strengthened to hold under this relaxed
assumption is therefore posed.Comment: 8 pages, re-written with new section
Time asymmetries in quantum cosmology and the searching for boundary conditions to the Wheeler-DeWitt equation
The paper addresses the quantization of minisuperspace cosmological models by
studying a possible solution to the problem of time and time asymmetries in
quantum cosmology. Since General Relativity does not have a privileged time
variable of the newtonian type, it is necessary, in order to have a dynamical
evolution, to select a physical clock. This choice yields, in the proposed
approach, to the breaking of the so called clock-reversal invariance of the
theory which is clearly distinguished from the well known motion-reversal
invariance of both classical and quantum mechanics. In the light of this new
perspective, the problem of imposing proper boundary conditions on the space of
solutions of the Wheeler-DeWitt equation is reformulated. The symmetry-breaking
formalism of previous papers is analyzed and a clarification of it is proposed
in order to satisfy the requirements of the new interpretation.Comment: 25 pages, 1 figur
No-Signalling Is Equivalent To Free Choice of Measurements
No-Signalling is a fundamental constraint on the probabilistic predictions
made by physical theories. It is usually justified in terms of the constraints
imposed by special relativity. However, this justification is not as clear-cut
as is usually supposed. We shall give a different perspective on this condition
by showing an equivalence between No-Signalling and Lambda Independence, or
"free choice of measurements", a condition on hidden-variable theories which is
needed to make no-go theorems such as Bell's theorem non-trivial. More
precisely, we shall show that a probability table describing measurement
outcomes is No-Signalling if and only if it can be realized by a
Lambda-Independent hidden-variable theory of a particular canonical form, in
which the hidden variables correspond to non-contextual deterministic
predictions of measurement outcomes. The key proviso which avoids contradiction
with Bell's theorem is that we consider hidden-variable theories with signed
probability measures over the hidden variables - i.e. negative probabilities.
Negative probabilities have often been discussed in the literature on quantum
mechanics. We use a result proved previously in "The Sheaf-theoretic Structure
of Locality and Contextuality" by Abramsky and Brandenburger, which shows that
they give rise to, and indeed characterize, the entire class of No-Signalling
behaviours. In the present paper, we put this result in a broader context,
which reveals the surprising consequence that the No-Signalling condition is
equivalent to the apparently completely different notion of free choice of
measurements.Comment: In Proceedings QPL 2013, arXiv:1412.791
Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations
In this talk we describe our recent work on discrete quantum theory based on
Galois fields. In particular, we discuss how discrete quantum theory sheds new
light on the foundations of quantum theory and we review an explicit model of
super-quantum correlations we have constructed in this context. We also discuss
the larger questions of the origins and foundations of quantum theory, as well
as the relevance of super-quantum theory for the quantum theory of gravity.Comment: 22 pages LaTeX. Uses ws-procs975x65.cls. Contribution to the
Proceedings of the Conference in Honour of the 90th Birthday of Freeman
Dyson, 26-29 August 2013, Institute of Advanced Studies at the Nanyang
Technological University, Singapore. Talk presented by Takeuch
Spin and Rotations in Galois Field Quantum Mechanics
We discuss the properties of Galois Field Quantum Mechanics constructed on a
vector space over the finite Galois field GF(q). In particular, we look at
2-level systems analogous to spin, and discuss how SO(3) rotations could be
embodied in such a system. We also consider two-particle `spin' correlations
and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless
not violated in this model.Comment: 21 pages, 11 pdf figures, LaTeX. Uses iopart.cls. Revised
introduction. Additional reference
Quantum theory without Hilbert spaces
Quantum theory does not only predict probabilities, but also relative phases
for any experiment, that involves measurements of an ensemble of systems at
different moments of time. We argue, that any operational formulation of
quantum theory needs an algebra of observables and an object that incorporates
the information about relative phases and probabilities. The latter is the
(de)coherence functional, introduced by the consistent histories approach to
quantum theory. The acceptance of relative phases as a primitive ingredient of
any quantum theory, liberates us from the need to use a Hilbert space and
non-commutative observables. It is shown, that quantum phenomena are adequately
described by a theory of relative phases and non-additive probabilities on the
classical phase space. The only difference lies on the type of observables that
correspond to sharp measurements. This class of theories does not suffer from
the consequences of Bell's theorem (it is not a theory of Kolmogorov
probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We
discuss its predictability properties, the meaning of the classical limit and
attempt to see if it can be experimentally distinguished from standard quantum
theory. Our construction is operational and statistical, in the spirit of
Kopenhagen, but makes plausible the existence of a realist, geometric theory
for individual quantum systems.Comment: 32 pages, Latex, 4 figures. Small changes in the revised version,
comments and references added; essentially the version to appear in Found.
Phy
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